Question: Multiply the following complex numbers: $({2i}) \cdot ({-i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2i}) \cdot ({-i}) = $ $ ({0} \cdot {0}) + ({0} \cdot {-1}i) + ({2}i \cdot {0}) + ({2}i \cdot {-1}i) $ Then simplify the terms: $ (0) + (0i) + (0i) + (-2 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 + 0)i - 2i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 + 0)i - (-2) $ The result is simplified: $ (0 + 2) + (0i) = 2 $